Permanent magnet synchronous motors (PMSM) are widely used in hybrid electric vehicles and battery electric vehicles. Among the permanent magnet synchronous motors, interior permanent magnet (IPM) motors are the most commonly used motors for HEV/BEV applications due to their high power density, high efficiency and wide speed range.
In automotive traction applications, operating an IPM motor at its maximum efficiency is necessary to maximize the use of the vehicle battery's limited power and energy. This can be achieved by optimizing the motor's control algorithm to provide maximum torque at a minimum motor current value. “Maximum torque per ampere” (MTPA) control algorithms maximize the IPM motor drive torque capability when the motor is operating below its rated speed. The MTPA control algorithms also minimize copper losses, thereby increasing the overall efficiency of the IPM motor (because copper losses are proportional to the square of the current).
Proper selection of the current vector is needed to develop an MTPA control algorithm. Referring to FIG. 1, the current vector is represented by the current magnitude ‘I’ and the current phase angle ‘α’ or, equivalently, by the d-axis current ‘Id’ and the q-axis current ‘Iq’ (in the Id-Iq axis plane). The current phase angle α is measured with respect to the positive Iq-axis in a counterclockwise direction with the d-axis current Id being equal to −I*Sin(α) and the q-axis current Iq being equal to I*Cos(α).
The torque of an interior permanent magnet motor is defined as:
                    T        =                                            3              ⁢              P                        2                    *                      [                                                            Φ                  mag                                *                I                *                                  Cos                  ⁡                                      (                    α                    )                                                              +                                                (                                      Lq                    -                    Ld                                    )                                *                                  I                  2                                *                                  Sin                  ⁡                                      (                    α                    )                                                  *                                  Cos                  ⁡                                      (                    α                    )                                                                        ]                                              (        1        )            Where P is the rotor pole pairs of the motor; Φmag is the permanent magnet flux; Ld is the d-axis inductance; and Lq is the q-axis inductance. The first term in Equation (1) represents the magnet torque and the second term represents the reluctance torque due to saliency (i.e., the difference between the d-axis and q-axis inductances).
To find the maximum torque per ampere, Equation (1) is differentiated with respect to the current and equated to zero. The optimal value of the current phase angle α at which the torque per current I becomes maximum is given below in Equation (2):
                    α        =                              sin                          -              1                                [                                                    -                                  ϕ                  mag                                            +                                                                                          (                                              ϕ                        mag                                            )                                        2                                    +                                      8                    *                                                                  (                                                  Ld                          -                          Lq                                                )                                            2                                        *                                          I                      2                                                                                                          4              *                              (                                  Ld                  -                  Lq                                )                            *              I                                ]                                    (        2        )            Where Ld and Lq vary depending on the phase angle α and the current magnitude I.
The MTPA trajectory is shown in FIG. 1. The MTPA trajectory points (I, α) correspond to the intersection between the constant current circles and the constant torque loci (given by Equation 1). The trajectory points P1, P2 and P3 correspond to the optimal operating points for torques T1, T2, T3. FIG. 1 illustrates one set of points (I, α), (Id, Iq) that correspond to point P1. It should be appreciated that there are points (I, α), (Id, Iq) that correspond to points P2 and P3 as well.
Generally, to use the MTPA algorithm described above, specific knowledge of three motor parameters is required (see Equation (2) above). These parameters are the d-axis inductance (Ld), q-axis inductance (Lq) and permanent magnet flux (Φmag). The relationship between the torque and motor currents in IPM motors, however, is non-linear (see Equation (1) above). Thus, any error in the estimation and computation of machine parameters will affect the control performance, resulting in less efficiency. Motor manufacturers do not provide operating range values for these parameters; even if they were provided, the parameters would only represent one operating point, which is not enough to optimize the control algorithm. The d-axis inductance (Ld), q-axis inductance (Lq) and permanent magnet flux (Φmag) parameters are non-linear and vary significantly as the machine is loaded; this presents a significant challenge in determining the minimum current magnitude for a given torque command.
Moreover, most of today's current IPM control schemes have additional shortcomings. For example, current online MTPA schemes are based on the injection of an additional pulsating current signal superimposed on a fundamental current vector, which causes additional copper losses, noise, vibration, torque pulsation and may cause additional problems in the control process. Most of the current online optimized MTPA schemes are based on derivatives, which are not very efficient and may get stuck in local minima/maxima during the optimization process. In addition, most of today's schemes use offline parameter estimation methods, which are very time consuming, not accurate and may increase control development time. Some of the schemes use online parameter estimation techniques that are computational intensive and become an additional burden on the processor while some parameter estimation schemes need additional hardware (e.g., filters) that may not be available and may increase control development time.
Accordingly, there is a need and desire for an optimized maximum torque per ampere control scheme for an interior permanent magnet motor, such as the IPM motors used in hybrid electric and battery electric vehicles.